问题
填空题
数列{an}，{bn}的通项公式满足：an•bn=1，且an=n2+3n+2，则数列{bn}的前10项之和是______．
答案
∵an•bn=1
∴bn=
=1 n2+3n+2 1 (n+1)(n+2)
∴s10=
+1 2×3
+ + 1 3×4
+1 10×11
=（1 11×12
-1 2
）+(1 3
-1 3
) + +(1 4
-1 10
) +(1 11
-1 11
)=1 12
-1 2
=1 12 5 12
故答案为
．5 12